Air does rise and go up. For example, hot air rises because when you heat air (or any other gas for that matter), it expands. When the air expands, it becomes less dense than the air around it. The less dense hot air then floats in the more dense cold air much like wood floats on water because wood is less dense than water. keep this in consideration though, as the hot air cools and sinks back to the surface of the earth, there it gets warmed by the ocean only to rise again. This is called a convection current. In conclusion, air does indeed rise and go up.